I have seen people cover their PCB and paint the heatsinks and ram slots. They suggested inserting and removing the ram/PCIe card several times to get the paint out.
But oh god please don't paint your AM3+ socket.

Since most oils are non-conductive, then that means this paint should be non-conductive as well?

Paints generally consist of four parts: Vehicle, Binder, Pigment and Fillers. The vehicle of the paint doesn't really matter as this evaporates leaving only the pigment , binder and fillers if any are used. Pigments and fillers are mainly what are going to cause a conductive issue as they tend to be metals and or metal oxides. Many years ago a hotrodder buddy of mine painted a bunch of his engine parts and then had issues. It turned out to be the red oxide (Iron Oxide) primer he used to base coat everything. One night we lifted his hood and you could see electricity arcing down around his distributor cap. Looked pretty cool but obviously he was having ignition problems. He painted another distributor cap using the paint only and did not have the problem.

P.S> I suggest being bold with your white statement and use fake spray snow.